Question 1145843: Rosa is 8 years younger than dale. if the product of their ages is 105,how old is each person
Found 4 solutions by VFBundy, MathTherapy, greenestamps, ikleyn:
Answer by VFBundy(438)   (Show Source):
You can put this solution on YOUR website! Dale = n
Rosa = n - 8
n(n - 8) = 105
n² - 8n = 105
n² - 8n - 105 = 0
(n + 7)(n - 15) = 0
n = -7, 15. Since n = -7 would make Dale's age (n) a negative number, we can eliminate this result. Therefore, we are left with n = 15.
Dale = n = 15
Rosa = n - 8 = 15 - 8 = 7
Answer by MathTherapy(10551)  (Show Source):
You can put this solution on YOUR website! Rosa is 8 years younger than dale. if the product of their ages is 105,how old is each person
Two FACTORS of 105 that differ by 8.
That all this is!!
Setting up a quadratic equations is SENSELESS, unless you're planning on using the quadratic equation formula or by completing the square.
These methods are more time-consuming so if you know how to find 2 such easy integers, then you can solve this in 2, 5, or maybe 10 seconds.
I did!!
You're right, @GREENESTAMPS. It should be 8 i/o 5. I corrected it though. Thanks.
Answer by greenestamps(13198)  (Show Source):
You can put this solution on YOUR website!
Tutor @MathTherapy is exactly right about how to solve this... although one number he shows in his explanation is a typo.
If you try to solve this problem using formal algebra, you end up with a quadratic equation; to solve that equation by factoring, you need to find two numbers whose product is 105 and whose difference is 8.
But that's what the original problem requires you to do!
So there is no point in using formal algebra -- unless this is an assignment where an algebraic solution is required.
Pairs of (whole) numbers whose product is 105:
105*1
35*3
21*5
15*7
Find the one for which the difference is 8....
Answer by ikleyn(52776)  (Show Source):
You can put this solution on YOUR website! .
Dear student (!)
After getting these posts from 3 tutors, you can be confused: to which way follow and whose advice to select.
First of all, you should not be in conflict with the teacher and the class policy.
Therefore, write a quadratic equation and solve it by any way: by factoring (if possible), or using the quadratic formula.
This guessing method is also good, and especially good to quickly guess the solution. You can use it
as your internal (interior) tool. But at the exam/quiz/test the quadratic equation is your tool #1,
if you need to show your work.
The mental "guessing" is your interior tool #2 <------> (notice, not #1, but #2) when you should present your work at the exam/quiz/test.
But in your "everyday mathematical exercises" you may use "guessing" to have your mind trained :)
It is good to quickly guess the solution, when possible, but it is not an issue to conflict with a teacher and a school.
It is good to have both methods in your possession, but it is not (again) an issue to conflict with a teacher and a school.
Short conclusion
1. The quadratic formula works always as an army tank, independently, if your roots are integer numbers,
or rational, or irrational, or even complex numbers.
2. Guessing works good in simple cases (integer roots; integer coefficients of the original equation).
3. In my practice, if I given a quadratic equation with integer coefficients and if I can not guess its solution in 5 - 7 seconds,
I switch my mind and use the quadratic formula.
4. If somebody tells you a story on how successfully he (or she) used guessing, always remember:
in complex / complicated cases it works especially good when the solution is known in advance.
This last my statement is a joke and a TRUTH at the same time :)
For many simple cases see my lesson
- Solving quadratic equations without quadratic formula
in this site.
Happy learning (!)
Come again to the forum soon to learn something new (!)
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